The first Shakespeare and Company, run by Sylvia Beach at rue de l'Odéon, was the base for Hemingway, Fitzgerald and the gang, but closed in the second world war. In 1951 George Whitman opened his own shop, Le Mistral, in a former 17th-century monastery overlooking Notre Dame. It became the base for Beat generation writers such as Burroughs and Ginsberg. He changed the name after Beach's death in 1962.

I stand outside. Its Seine-side location is idyllic, even on a freezing February morning, with workmen on ladders outside its bottle-green facade, mending the electricals, and a skeletal tree wreathed in a string of bulbs. Summer must be wonderful here: there are empty garden chairs strewn between trays of hardy books.

28-year-old Sylvia Whitman, George's daughter, has agreed to show me round. Signs at the entrance marked "Beat" and "Lost" are a reminder of both stores' heavyweight associations. A wishing well, around which a handful of customers shuffle, glistens with pennies.

Her father, Sylvia says, hoped to work until he was 100 but, forced to retire at 93, now lives on the second floor. He no longer gives interviews. We wander past shelves devoted to fiction, biography, art and French interest. "It's more organised that it looks," she says, with a laugh.

Paperbacks line red wooden steps leading upstairs to what Sylvia calls the "non-commercial" floor: a library in which you could lose yourself, with one rule: books mustn't leave the premises. Here, as on the ground floor, single mattresses lurk between the shelves, and, in the children's section, a bunk bed. It's on these that young authors sleep each night.

"We have six at any one time," says Sylvia, "generally in their early 20s. They come to write from all over the world while doing a couple of hours in the shop a day. Generally they stay a week to a month, but one English poet stayed seven years." Seven years – really? "If someone's reading and writing, we encourage that," she says. "It's a different life after closing time. They all come out of the woodwork! And for us, it's an organic cycle: aspiring writers tapping away upstairs and books being sold downstairs."

Everything here encourages creativity. A tiny enclosed bureau, lined with rugs and a blue painted chair, bears the sign: "Feel free to use the typewriter for your lovely writing/creative ventures." Notes from customers are scrawled in all languages. "A friend told me if I ever felt lonely to come to Shakespeare & Company," one says. Visitors are so effusive that a few years ago George installed what he calls a "mirror of love", where hundreds more scribblings are pinned, from the surreal to the touching: "Dear Granny, I would like you to come to Paris with me", reads one. "Books insulate this nest of wandering dreams", reads another, "there should always be a place where stories reign over commercial enterprise."

We stand in the beamed reading room, the light soupy. George's mongrel, Collette, smart in a red neckerchief, snoozes on a rug lining the stone floor. A white cat arches its back on a desk overlooking the river. Sylvia explains that when it rains the room fills with readers and writers, all jostling for the handful of cushions scattered along the wooden banquette. Her image only sharpens the silence of this morning.

As I leave, the western facade of Notre Dame is noisy with tourists. I cross the square, haunted by one of the messages tacked to the mirror. Hand-written by the mother of a 21-year-old bipolar man who killed himself by jumping off Brooklyn Bridge, it read: "I've spent the last hour trying to decide if I should end my life. If he could have discovered your bookshop, perhaps he would have survived. I want to thank you for this place and the hope it gives." Not only does that seem to underline the redemptive power of literature, but also something less tangible: the balm of environment.